$($a$)$ A cellular system has a total bandwidth of $30MHz.$ Each full duplex voice channel

uses two $25kHz$ simplex channels. The system uses a $9-$cell reuse pattern and $0\mathrm{.}75$

$MHz$ from the total bandwidth is allocated for control channels. The system service

area consists of $50$ cells. It is a blocked system with a call blocking probability of

$2\%.$ If the offered traffic of each user is $0\mathrm{.}025$ Erlang, calculate:

$($i$)$ the traffic load in each cell and the trunking efficiency,

$($ii$)$ the total number of users in each cell and in the system, respectively,

$($iii$)$ the number of users per channel in each cell and in the system, and

$($iv$)$ the maximum number of users in service at any instant in the system.

$(16$ Marks$)$

$($b$)$ The frequency reuse factor for a cellular system is given by $\frac{S}{J}$ where $J$ is the

number of channels per cell and $S$ is the total number of channels available for the

entire cellular network. Each cluster can be replicated $C$ times to provide a total

capacity of $T$ channels. If $S$ is constant, discuss the changes of the value of $T$ when

increasing or decreasing the frequency reuse factor.

$(12$ Marks$)$

$($c$)$ Considering a cellular system with hexagonal cells, each with cell radius $R.$ The

service area is partitioned into clusters. Frequency is reused. Derive the distance $D$

between the centers of two adjacent co$-$channel cells and the number of cells $N$ in

each cluster.

$(12$ Marks$)$